Description
Advanced Mathematical Tools for Control Engineers: Volume 1 provides a blend of Matrix and Linear Algebra Theory, Analysis, Differential Equations, Optimization, Optimal and Robust Control. It contains an advanced mathematical tool which serves as a fundamental basis for both instructors and students who study or actively work in Modern Automatic Control or in its applications. It is includes proofs of all theorems and contains many examples with solutions.It is written for researchers, engineers, and advanced students who wish to increase their familiarity with different topics of modern and classical mathematics related to System and Automatic Control Theories.- Provides comprehensive theory of matrices, real, complex and functional analysis- Provides practical examples of modern optimization methods that can be effectively used in variety of real-world applications- Contains worked proofs of all theorems and propositions presented
Table of Contents
I MATRICES AND RELATED TOPICS1 Determinants2 Matrices and Matrix Operations 3 Eigenvalues and Eigenvectors 4 Matrix Transformations 5 Matrix Functions 6 Moore-Penrose Pseudoinverse 7 Hermitian and Quadratic Forms8 Linear Matrix Equations 9 Stable Matrices and Polynomials 10 Algebraic Riccati Equation 11 Linear Matrix Inequalities 12 MiscellaneousII ANALYSIS 13 The Real and Complex Number Systems14 Sets, Functions and Metric Spaces 15 Integration 16 Selected Topics of Real Analysis17 Complex Analysis 18 Topics of Functional Analysis III DIFFERENTIAL EQUATIONS AND OPTIMIZATION19 Ordinary Differential Equations 20 Elements of Stability Theory 21 Finite-Dimensional Optimization 22 Variational Calculus and Optimal Control 23 H2 and H∞ Optimization 811
